We propose a novel photonic approach to implementing instantaneous microwave frequency measurement with improved measurement range and resolution. A polarization modulator (PolM) is employed, which functions with a polarizer as an intensity modulator (IM) in one channel, and with a length of polarization-maintaining fiber as a two-tap photonic microwave bandpass filter (PMBF) in another channel. A linear amplitude comparison function (ACF) that relates the microwave frequency and the microwave powers at the outputs of the two channels is obtained, which ensures an improved frequency measurement range and resolution. An experiment is performed. A measurement range of 0.5-40 GHz with a resolution of ±0.5 GHz under different input microwave power levels is realized.